I had $30 in allowance money and spent it as indicated in the pie graph shown. How many dollars did I spend on burgers? [asy] size(150); pair A, B, C, D, O, W, X, Y, Z; O=(0,0); A=(.707,.707); B=(-.966,.259); C=(-.707,-.707); D=(.342,-.940); draw(Circle(O, 1)); draw(O--A); draw(O--B); draw(O--C); draw(O--D); W=(-.1,.5); label("Movies", W, N); label("$\frac{1}{3}$", W, S); X=(-.55, 0); label("Burgers", X, S); Y=(-.17,-.7); label("Ice Cream", Y, N); label("$\frac{1}{5}$", Y, S); Z=(.5, -.15); label("Music", Z, N); label("$\frac{3}{10}$", Z, S); [/asy]
Because $\frac{1}{3}$ of the money was spent on movies and there is 30 dollars, the amount of money spent on movies is $\frac{1}{3} \cdot 30=10$ dollars. Likewise, $\frac{3}{10} \cdot 30=9$ dollars were spent on music and $\frac{1}{5} \cdot 30 = 6$ dollars were spent on ice cream. Thus, the total amount of money spent on movies, music, and ice cream is $\$10+\$9+\$6=\$25$. The remaining amount of money is spent on burgers. Thus, the money spent on burgers is $\$30-\$25=\$\boxed{5}$.